A Reifenberg type characterization for $m$-dimensional $C^1$-submanifolds of $\mathbb R^n$
Differential Geometry
2018-04-17 v2
Abstract
We provide a Reifenberg type characterization for -dimensional -submanifolds of . This characterization is also equivalent to Reifenberg-flatness with vanishing constant combined with suitably converging approximating -planes. Moreover, a sufficient condition can be given by the finiteness of the integral of the quotient of -numbers and the scale , and examples are presented to show that this last condition is not necessary.
Keywords
Cite
@article{arxiv.1804.02187,
title = {A Reifenberg type characterization for $m$-dimensional $C^1$-submanifolds of $\mathbb R^n$},
author = {Bastian Käfer},
journal= {arXiv preprint arXiv:1804.02187},
year = {2018}
}